16 ideas
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
18087 | If x changes by less and less, it must approach a limit [Dedekind] |
18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |